Consider, for example, the linear congruence:
$56x \equiv 23 ($mod $93)$ if we know that the inverse of of $56$ modulo $93$ is $5$.
Multiplying both sides by the inverse, $5$, we have: $280 x \equiv 115 ($mod $93)$.
Thus: $x \equiv 115($mod $93)$.
From here on, I do not know how to solve it.